List of Figures

View Image Figure 1:
Magnetic forces play a key role in solar storms that can impact Earth’s magnetic shield (magnetosphere) and create colorful aurora. Image courtesy of External LinkSOHO (ESA & NASA).
View Image Figure 2:
Plasma β model over active regions. The shaded area corresponds to magnetic fields originating from a sunspot region with 2500 G and a plage region with 150 G. The left and right boundaries of the shaded area are related to umbra and plage magnetic field models, respectively. Atmospheric regions magnetically connected to high magnetic field strength areas in the photosphere naturally have a lower plasma β. Image reproduced by permission from Figure 3 of Gary (2001), copyright by Springer.
View Image Figure 3:
Global potential field reconstruction. Image reproduced by permission from Wiegelmann and Solanki (2004), copyright by ESA.
View Image Figure 4:
How to obtain the optimal linear force-free parameter α from coronal observations. Image reproduced by permission from Figures 3, 4, and 5 of Carcedo et al. (2003), copyright by Springer.
View Image Figure 5:
Low and Lou’s (1990) analytic nonlinear force-free equilibrium. The original 2D equilibrium is invariant in φ, as shown in panel a. Rotating the 2D-equilibrium and a transformation to Cartesian coordinates make this symmetry less obvious (panels b–d), where the equilibrium has been rotated by an angle of π π φ = 8 ,4, and π 2, respectively. The colour-coding corresponds to the vertical magnetic field strength in G (gauss) in the photosphere (z = 0 in the model) and a number of arbitrary selected magnetic field lines are shown in yellow.
View Image Figure 6:
Construction of the Titov–Démoulin equilibrium. Image reproduced by permission from Figure 2 of Titov and Démoulin (1999), copyright by ESO.
View Image Figure 7:
Overview of the performance of different algorithms for removing the 180° azimuth ambiguity. The codes have been applied to synthetic data (a flux-rope simulation by Fan and Gibson, 2004). In black areas the codes found the correct azimuth and in white areas not. Image reproduced by permission from Figure 3 of Metcalf et al. (2006), copyright by Springer.
View Image Figure 8:
Magnetic helicity of field lines in torus configuration: untwisted (left), twisted by T turns (middle), and two untwisted but intersecting tori (right). Φ stands for the total magnetic flux.
View Image Figure 9:
Numerical simulations starting from an unstable branch of the Titov–Démoulin equilibrium in comparison with TRACE observations of an eruption. Image reproduced by permission from Figure 1 of Török and Kliem (2005), copyright by AAS.
View Image Figure 10:
A series of coaligned images of AR 10953. Blue lines are stereoscopically-reconstructed loops (Aschwanden et al., 2008b). Red lines are extrapolated nonlinear force-free field lines from Hinode/SOT with MDI data outside the Hinode FOV (the dotted line). Image reproduced by permission from Figure 1 of DeRosa et al. (2009), copyright by AAS.
View Image Figure 11:
Yohkoh soft X-ray image overlaid with magnetic field lines from different models. Top: nonlinear force-free; center: linear force-free; bottom: potential fields. Image reproduced by permission from Figure 8 of Bleybel et al. (2002), copyright by ESO.